Testing Experimental Treatment for Prostate Cancer

This is an unblinded, randomized clinical study comparing the efficacy of DNA damaging chemotherapy using carboplatin, to standard of care chemotherapy for patients who have metastatic castrate resistant prostate cancer. This trial will use docetaxel or carboplatin as initial chemotherapy with crossover to the alternate or second-line drug after first progression for patients with tumors containing BRCA1, BRCA2 or PALB2 inactivating DNA mutations. Participants are randomized (1:1) and receive either carboplatin (AUC 5) first or docetaxel (75 mg/m2) every 21 days until intolerance, complete response, or progression by Prostate Cancer Working Group 3 (PCWG3) criteria or 10 cycles (whichever is first). Participants then crossover from the first-line therapy to the second-line therapy with the opposite study medication and receive treatment to intolerance or progression or 10 cycles (whichever is first). Enrolled participants will be allowed to crossover to second line therapy if they continue to meet initial eligibility criteria, and at least three weeks have elapsed since last administration of either carboplatin or docetaxel. Throughout the study, safety and tolerability will be assessed. Progression will be evaluated with bone scan, CT of the abdomen/pelvis, or MRI and PSA as per PCWG3 criteria.